Problem: Rewrite as a simplified fraction. ${2.6\overline{53} = {?}}$
Answer: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 2653.5353...\\ 10x &= 26.5353...\end{align*}}$ Subtracting the two equations, we have: ${990x = 2627}$ ${x = \dfrac{2627}{990}} \text{or} {2 \dfrac{647}{990}}$